A general method for determining the radius of curvature of an object's surface is based on a differential measuring technique. In the differential measuring technique, a technician positions a reference element and the object to form a retroreflecting cavity by centering each element on an optical centerline and orienting the two elements so that they are parallel to each the other. A retroreflecting cavity forms when the two elements are spaced apart such that collimated light entering the cavity through the reference element is brought to a focus on the surface of either the element or object. The null order of the retroreflecting cavity characterizes how many times a light ray entering the cavity parallel to but off-axis with respect to the optical centerline, bouncing between the reference element and the object and intersecting the optical axis at either the reference element or object, strikes the surface of the object before it exits the cavity parallel to but off-axis with respect to the optical centerline. The null order changes as the object having a single radius of curvature is translated closer to or away from the reference element. The radius of curvature is calculated via a paraxial ray approximation by measuring the distance in cavity length between successive null orders. Differential techniques for measuring radii of curvature are discussed, for example, in “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces” published in SPIE, 192, 75-84, 1979.
Typically, radii measurement techniques such as those described above required time consuming and error generating manual adjustments in determining the radius of curvature of an object.